基于OpenFOAM的磁流体求解器的开发和应用

基于计算流体力学平台OpenFOAM,本文开发了一套可压缩磁流体求解器,并将其应用于二维和三维的跨音速束流模拟.该求解器对OpenFOAM自带的密度基中心差分黎曼求解器rhoCentralFoam进行了修改,植入一个隐式压力分离算法用以控制磁场散度误差并保证模拟结果的数值精度.本文对此求解器进行了检测,证明了它的收敛阶在1—2之间,并将其应用到强激光等离子体的磁流体模拟.利用该求解器,本文讨论了外加均匀轴向磁场对激光等离子体喷流的影响,发现了喷嘴和结节位置与热压比开方之间的线性关系.本文还分析了电容线圈中产生的非均匀磁场对激光等离子体喷流的影响.初步模拟结果表明,当线圈中心磁场相同时,小尺寸线圈产生的磁场会加快喷嘴和结节的形成,等效的均匀轴向磁场更大.此模拟结果可以作为我们将来的磁化喷流实验的参考.同时,这样物理结果表明该磁流体求解器适合做面向激光等离子体实验的工程计算,可以应对构型比较复杂的场合.     

高密高温等离子体中类氢炭静电屏蔽势的求解

在离子球模型下,本文通过对Poisson方程和Dirac-Fock方程的自恰求解,计算得到了不同电子密度下类氢炭周围的Coulomb静电屏蔽势.该静电屏蔽是对于理解高密度等离子体中的原子结构、等离子体中各种碰撞过程及等离子体模拟具有重要意义.     

高密高温等离子体中类氢炭静电屏蔽势的求解

在离子球模型下，本通过对Poisson方程和Dirac-Fock方程的自恰求解，计算得到了不同电子密度下类氢炭周围的Coulomb静电屏蔽势。该静电屏蔽是对于理解高密度等离子体中的原子结构、等离子体中各种碰撞过程及等离子体模拟具有重要意义。     

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从Lagrange观点出发,采用分裂格式法求解一维辐射流体力学方程组中的三温方程,用于紧凑等离子体环与靶碰撞产生的X射线辐射的数值模拟研究。提出了求解电子、离子、辐射场三温相脱离的能量方程的隐式差分格式,介绍了能量交换项与压力做功及热传导项分开计算的分裂格式方法,数值模拟得到了其对温度变化的影响。     

等离子体电极普克尔盒电光开关单脉冲过程数值模拟

采用流体模型对等离子体电极普克尔盒(PEPC)电光开关单脉冲过程进行了数值模拟分析.模型包括带电粒子连续性方程、动量守恒方程、电子平均能量方程及空间电位泊松方程.分别采用隐式指数差分格式，超松弛迭代法(SOR)和经典四阶龙格-库塔法(R-K)对带电粒子连续性方程，泊松方程和电子平均能量方程进行数值求解.模拟分析了PEPC单脉冲过程中的带电粒子浓度、电子温度、空间电场、PEPC的放电电流、晶体两侧电压和开关效率的时间演化特性.模型得出了PEPC中气体放电等离子体的微观物理过程与PEPC宏观参量的关系，对设计 关键词： 等离子体电极普克尔盒 电光开关 数值模拟 气体放电     

热辐射输运问题的隐式蒙特卡罗方法求解

热辐射与物质相互作用及辐射光子在物质中的传输是惯性约束聚变研究中的重要课题. 介绍了基于隐式蒙特卡罗方法的辐射输运方程,在该方程的积分-微分形式基础上,推导了利于蒙特卡罗方法模拟的等价的积分输运方程;基于积分方程设计数值模拟流程,编写三维蒙特卡罗数值模拟程序;针对热辐射输运典型问题及benchmark问题开展了数值实验,计算结果验证了方法的适应性及程序的正确性. 关键词： 热辐射 惯性约束聚变 输运方程 隐式蒙特卡罗     

快点火中相对论电子束能量沉积的动理学研究

针对相对论快电子束在高密度压缩芯区等离子体中的能量沉积过程开展物理建模、程序研制和数值模拟研究。从等离子体粒子碰撞的基本物理出发,综合考虑了高能电子与背景等离子体之间的短程两体碰撞过程和长程集体效应,建立了相对论Fokker-Planck动理学模型,通过采用球谐展开的方法,推导得到了适于数值求解的方程形式并根据方程特点开展相应的数值算法研究及程序研制并完成了物理考核,对快点火能量沉积的典型物理算例进行了模拟研究,并针对即将在神光Ⅱ升级装置上开展的快点火物理实验进行了初步的物理分析。     

粒子输运离散纵标方程基于界面修正的并行计算方法

为了改造粒子输运方程求解的隐式格式,研究设计适应大型并行计算机的并行计算方法,介绍一类求解粒子输运方程离散纵标方程组的基于界面修正的源迭代并行计算方法.应用空间区域分解,在子区域内界面处首先采用迎风显式差分格式进行预估,构造子区域的入射边界条件,然后,在各个子区域内部进行源迭代求解隐式离散纵标方程组.在源迭代过程中,在内界面入射边界处采用隐式格式进行界面修正.数值算例表明该并行计算方法在精度、并行度、简单性诸方面均具有良好的性质.     

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针对磁约束聚变等离子体边缘湍流中非线性能量传递过程的问题,开发了数据分析程序.该程序基于数字谱分析技术来求解波耦合方程,进而计算与三波相互作用相关联的线性和非线性耦合系数以及能量转移.介绍了算法设计和程序开发的主要思想,并对程序进行了仿真测试.然后应用该程序分析了反场箍缩装置实验的一次放电实验数据,观察到湍流之间的波耦合和能量级联现象,发现或证实了聚变等离子体湍流激发与增长的一种内在机制.     

基于谱估计方法的等离子体湍流三波耦合数据处理算法

基于数字谱分析技术求解波耦合方程,进而计算与三波相互作用相关联的线性耦合系数和能量转移,以此开发了数据处理程序用于研究HL-2A 装置等离子体边缘湍流中的非线性能量传递过程。介绍了算法设计和开发的主要思想。应用该程序对与带状流相关的一次放电的实验数据进行了数据处理研究。结果表明,带状流是由等离子体湍流的能量逆级联所驱动的。     

ISSDE: A Monte Carlo implicit simulation code based on Stratonovich SDE approach of Coulomb collision

A Monte Carlo implicit simulation program, Implicit Stratonovich Stochastic Differential Equations(ISSDE), is developed for solving stochastic differential equations(SDEs) that describe plasmas with Coulomb collision. The basic idea of the program is the stochastic equivalence between the Fokker–Planck equation and the Stratonovich SDEs. The splitting method is used to increase the numerical stability of the algorithm for dynamics of charged particles with Coulomb collision. The cases of Lorentzian plasma, Maxwellian plasma and arbitrary distribution function of background plasma have been considered. The adoption of the implicit midpoint method guarantees exactly the energy conservation for the diffusion term and thus improves the numerical stability compared with conventional Runge–Kutta methods. ISSDE is built with C++ and has standard interfaces and extensible modules. The slowing down processes of electron beams in unmagnetized plasma and relaxation process in magnetized plasma are studied using the ISSDE, which shows its correctness and reliability.     

Modeling of beam ions loss and slowing down with Coulomb collisions in EAST

This paper uses the implicit Monte-Carlo full-orbit-following parallel program ISSDE to calculate the prompt loss and slowing down process of neutral beam injection (NBI)-generated fast ions due to Coulomb collisions in the equilibrium configuration of Experimental Advanced Superconducting Tokamak (EAST). This program is based on the weak equivalence of the Fokker-Planck equation under Rosenbluth MacDonald Judd (RMJ) potential and Stratonovich stochastic differential equation (SDE). The prompt loss with the LCFS boundary and the first wall (FW) boundary of the two co-current neutral injection beams are studied. Simulation results indicate that the loss behavior of fast ions using the FW boundary is very different from that of the LCFS boundary, especially for fast ions with a large gyration radius. According to our calculations, about 5.11% of fast ions generated by perpendicular injection drift out of the LCFS and then return inside the LCFS to be captured by the magnetic field. The prompt loss ratio of fast ions and the ratio of orbital types depend on the initial distribution of fast ions in the P_ζ-$\varLambda$ space. Under the effect of Coulomb collisions, the pitch-angle scattering and stochastic diffusion happens, which will cause more fast ion loss. For short time scales, among the particles lost due to collisions, the fraction of banana ions reaches 92.31% in the perpendicular beam and 58.65% in the tangential beam when the fraction of banana ions in the tangential beam is 3.4% of the total ions, which means that the effect of Coulomb collisions on banana fast ions is more significant. For long time scales, the additional fast ion loss caused by Coulomb collisions of tangential and perpendicular beams accounted for 16.21% and 25.05% of the total particles, respectively. We have also investigated the slowing down process of NBI fast ions.     

Elimination of Fast Variables for a Class of Nonlinear Stochaqtic Dynamical Systems

A set of nonlinear stochastic differential equations (NSDE's) that describes a large class of nonlinear stochastic dynamical systems is studied. By virtue of the stochastic generalization of. usual adiabatic approximation, we obtain the solution of equation for the fast variable, and obtain a closed equation for the slow variable. The statistical properties of the-new stochastic variables occurred are studied. The formal NSDE's are treated in the Stratonovich sense and the Ito sense respectively.     

Mathematical problems of modeling stochastic nonlinear dynamic systems

The purpose of this report is to introduce the engineer to the area of stochastic differential equations, and to point out the mathematical techniques and pitfalls in this area. Topics discussed include continuous-time Markov processes, the Fokker-Planck-Kolmogorov equations, the Ito and Stratonovich stochastic calculi, and the problem of modeling physical systems.     

Conserved quantities and symmetries related to stochastic Hamiltonian systems

In this paper symmetries and conservation laws for stochastic dynamical systems are discussed in detail. Determining equations for infinitesimal approximate symmetries of Ito and Stratonovich dynamical systems are derived. It shows how to derive conserved quantities for stochastic dynamical systems by using their symmetries without recourse to Noether's theorem.     

Langevin equations and stochastic integrals

The ambiguity of stochastic integrals involved in Langevin equations is removed by the postulate of invariance with respect to nonlinear transformations of the coordinates. The Stratonovich sense of the integrals, which is imposed thereby, is also strongly suggested by stability considerations requiring small changes of the solutions whenever the perturbations are changed by a small amount. The associated Fokker-Planck equation must include the spurious drift which arises from the transition from the Stratonovich to the Itô sense of the Langevin equations and describes one aspect of the systematic motion due to nonconstant fluctuations.     

On the equivalence between different methods of modelling diffusion processes

For a damped harmonic oscillator with frequency fluctuations it is shown that the phenomenological modelling of this system using the Stratonovich interpretation of stochastic differential equations leads to the same Fokker-Planck equation as the analysis of this system by means of projector techniques.     

Micromagnetic simulation of thermally activated switching in fine particles

Effects of thermal activation are included in micromagnetic simulations by adding a random thermal field to the effective magnetic field. As a result, the Landau–Lifshitz equation is converted into a stochastic differential equation of Langevin type with multiplicative noise. The Stratonovich interpretation of the stochastic Landau–Lifshitz equation leads to the correct thermal equilibrium properties. The proper generalization of Taylor expansions to stochastic calculus gives suitable time integration schemes. For a single rigid magnetic moment the thermal equilibrium properties are investigated. It is found, that the Heun scheme is a good compromise between numerical stability and computational complexity. Small cubic and spherical ferromagnetic particles are studied.     

Ito versus stratonovich revisited

It is shown that a digital simulation of a noise induced phase transition using an algorithm consistent with the Ito stochastic calculus is in agreement with the predictions of that theory, whereas experiments with an analogue simulator yield measured results in agreement with the predictions of the Stratonovich theory.     

Quantum stochastic differential equations for boson and fermion systems—method of non-equilibrium thermo field dynamics

A unified canonical operator formalism for quantum stochastic differential equations, including the quantum stochastic Liouville equation and the quantum Langevin equation both of the Itô and the Stratonovich types, is presented within the framework of non-equilibrium thermo field dynamics (NETFD). It is performed by introducing an appropriate martingale operator in the Schrödinger and the Heisenberg representations with fermionic and bosonic Brownian motions. In order to decide the double tilde conjugation rule and the thermal state conditions for fermions, a generalization of the system consisting of a vector field and Faddeev-Popov ghosts to dissipative open situations is carried out within NETFD.